Upload
dangcong
View
219
Download
4
Embed Size (px)
Citation preview
Quadratics:Factoring
Polynomials
Name:________________________
Steps:
1. GCF – Any number of terms
2. Four Terms – Grouping
3. Three Terms – Trinomial Rules
4. Two Terms – Difference of 2 Squares
Greatest Common Factora. 3x2 + 15x
b. 10a2 + 4a
c. 14m2n – 2mn
Four Terms – Grouping
a. y3 + 7y2 + 2y + 14
b. x3 – 4x2 – 6x + 24
c. x(x + 2) – 12(x + 2)
Sign Rules
Factoring Trinomials Sign Rules
If the last term is POSITIVE:
If the last term is NEGATIVE:
Both signs will be the SAME as the middle
term.
Signs will be DIFFERENT in the
parentheses.
( + )( + )or
( −¿ )( −¿ )( + )( −¿ )
If b is POSITIVE, then the larger factor needs to be positive
If b is NEGATIVE, then the larger factor will need to be
Three Terms – Trinomials when a = 1a. x2 + 10x + 16
b. x2 – 12x + 27
c. 2m2 + 4m – 48
d. –n2 + 12n - 36
Three Terms – Trinomials when a > 1a. 3y2 + 5y + 2
b. 2m2 + m – 21
c. 6x2 – 13x + 2
Perfect Trinomialsa. n2 – 12n + 36
b. x2 + 10x + 25
c. a2 – 2a + 1
Two Terms – Difference of Squares
a. x2 – 25
b. 2t2 – 8
c. x2 + 36
d. 4x2 – 25
e. 49 – 9m2
ALWAYS in the form: (x + y)(x – y)Think conjugates to cancel the middle terms!
Solve by Square Rootsa. x2 – 7 = 9 b. 4r2 – 7 = 9
c. 36x2 = 121 d. 7x2 – 8 = 13
e. 4z2 + 7 = 12 f. (x + 2)2 = 10
g. 2(x – 3)2 = 18
Solve by Quadratic Formulax=−b±√b2−4ac
2a
a. x2 + 7x + 12 = 0 b. 4x2 – 4x + 1 = 0
c. 4x2 + 8x – 1 d. -2x2 – 2x = 1
Completing the Squarea. x2 – 10x + 13 = 0
b. x2 – 8x + 7 = 0
c. 3x2 – 12x + 27 = 0
d. 2x2 – 20x + 24 = 0